Results 71 to 80 of about 1,625,058 (297)
Another Riemann Hypothesis Equivalent [PDF]
arXiv, 2021 Identities involving Mobius function values (u(j),u(k)) are used to generate a Riemann Hypothesis equivalent.
arxiv
On Balazard, Saias, and Yor's equivalence to the Riemann Hypothesis
, 2013 Balazard, Saias, and Yor proved that the Riemann Hypothesis is equivalent to a certain weighted integral of the logarithm of the Riemann zeta-function along the critical line equaling zero.
Bui, H. M. +2 more
core +1 more source
ESC Heart Failure, EarlyView.Abstract Aims Heart failure (HF) is one of today's leading public health issues worldwide. The sodium‐glucose cotransporter 2 inhibitor (SGLT2i) dapagliflozin recently received a label expansion. It is now approved for treatment of HF across the entire spectrum of ejection fraction (EF) in Germany. However, real‐world data are limited.
Matthias Paul +7 more
wiley +1 more source
Academic Burden and Emotional Problems Among Adolescents: A Longitudinal Mediation Analysis
Journal of Adolescence, EarlyView.ABSTRACT Introduction Existing research indicates high prevalence of emotional problems among adolescents with excessive academic burden, yet the underlying reasons are not well understood. This study aimed to explore loneliness, physical activity, and sleep as potential mediating pathways between academic burden and emotional problems in adolescents ...
Jingyi Wang +7 more
wiley +1 more source
Disproof of the Riemann hypothesis
, 2022 Let Theta be the supremum of the real parts of the zeros of the Riemann zeta function. We demonstrate in this note that Theta=1. This entails the existence of infinitely many zeros of zeta(s) off the critical line Re(s) = 1/2, which disproves the Riemann hypothesis.
openaire +1 more source
Aquatic heatwaves increase surface chlorophyll concentrations in experimental and reference lakes
Limnology and Oceanography Letters, EarlyView.Abstract Aquatic heatwaves are increasing in frequency, intensity, and duration worldwide. While increases in mean water temperatures are linked to enhanced phytoplankton biomass, it is unclear how heatwaves alter phytoplankton dynamics in lakes at an ecosystem scale.
Daniel K. Szydlowski +3 more
wiley +1 more source
A canonical system of differential equations arising from the Riemann zeta-function [PDF]
, 2016 This paper has two main results, which relate to a criteria for the Riemann hypothesis via the family of functions $\Theta_\omega(z)=\xi(1/2-\omega-iz)/\xi(1/2+\omega-iz)$, where $\omega>0$ is a real parameter and $\xi(s)$ is the Riemann xi-function. The
Suzuki, Masatoshi
core
Remarks on the Connection of the Riemann Hypothesis to Self-Approximation
ComputationBy the Bagchi theorem, the Riemann hypothesis (all non-trivial zeros lie on the critical line) is equivalent to the self-approximation of the function ζ(s) by shifts ζ(s+iτ).
Antanas Laurinčikas
doaj +1 more source
Prime numbers with a certain extremal type property
Annales Universitatis Paedagogicae Cracoviensis: Studia Mathematica, 2019 The convex hull of the subgraph of the prime counting function x → π(x) is a convex set, bounded from above by a graph of some piecewise affine function x → ε(x). The vertices of this function form an infinite sequence of points (ek,π(ek))1∞.
Edward Tutaj
doaj +1 more source
Error term of the mean value theorem for binary Egyptian fractions
Open Mathematics, 2020 In this article, the error term of the mean value theorem for binary Egyptian fractions is studied. An error term of prime number theorem type is obtained unconditionally. Under Riemann hypothesis, a power saving can be obtained.
Xiao Xuanxuan, Zhai Wenguang
doaj +1 more source